Luckily, the Fire's low price and popularity relative to other Android tablets has made it a common target for Android's bustling open-source community, which has automated most of the sometimes-messy process of rooting and flashing your tablet. The Kindle Fire Utility boils the whole rooting process down to a couple of steps, and from there it's pretty easy to find pretty-stable Jelly Bean ROMs. A CyanogenMod-based version is actively maintained, but I prefer the older Hashcode ROM, which is very similar to the interface on the Nexus 7.
http://yro.slashdot.org/story/12/10/...rs-kindle-fire